[tex]\it a)\ \ ab=144 \ \ \ \ (1)\ \ \ \ \ bc=225\ \ \ \ (2)\\ \\ \\ a(b+c)=340 \Rightarrow ab+ac=340\ \stackrel{(1)}{\Longrightarrow}144+ac=340\bigg|_{-144} \Rightarrow ac=196\ \ \ \ (3)\\ \\ \\ (1),\ (2),\ (3) \Rightarrow ab\cdot bc\cdot ac=144\cdot225\cdot196 \Rightarrow a^2\cdot b^2\cdot c^2=12^2\cdot15^2\cdopt14^2 \Rightarrow\\ \\ \\ \Rightarrow a\cdot b\cdot c = 12\cdot15\cdot14=2520[/tex]
b)
[tex]\it \overline{ab}:\overline{ba}=2\ \ rest\ 15 \Rightarrow \overline{ab}=2\overline{ba}+15 \Rightarrow 10a+b=2(10b+a)+15 \Rightarrow \\ \\ \\ \Rightarrow 10a+b=20b+2a+15 \Rightarrow 10a-2a=20b+15-b \Rightarrow 8a=19b+15\ \ \ \ (*)\\ \\ \\ 8a=par\ \stackrel{(*)}{\Longrightarrow}\ b=impar \\ \\ \\ b=1\ \stackrel{(*)}{\Longrightarrow} 8a=19+15 \Rightarrow 8a=34,\ nu\ convine\\ \\ \\ b=3 \stackrel{(*)}{\Longrightarrow} 8a=57+15 \Rightarrow 8a=72 \Rightarrow a=9[/tex]
Pentru celelalte valori impare ale cifrei b, nu se obține o cifră pentru a.
Așadar, numărul cerut este 93 .
